# Research

## Published Papers

• Semyon Malamud and Grigory Vilkov. Non-Myopic Betas, forthcoming in Journal of Financial Economics, 2017

## Working Papers

• Adrian Buss, Lorenzo Schoenleber, and Grigory Vilkov (2017). Expected Stock Returns and the Correlation Risk Premium, available shortly

Abstract: We develop and test a new methodology for out-of-sample forecasts of the aggregate market return, based on variance and correlation risk premiums. Estimating correlation and variance betas from the joint dynamics of option-implied variables and index returns, we find significant \emph{out-of-sample} $R^2$'s of $13\%$ and $7\%$ for 3- and 12-months forecast horizons, respectively. While the predictability of the variance risk premium is strongest at the intermediate, quarterly month horizon, the correlation risk premium dominates at the longer horizons. In line with a risk-based explanation for the existence of a correlation risk premium, we document that contemporaneous implied and lagged realized correlations predict future diversification risks, in terms of the future average correlation and the non-diversifiable portfolio market exposure.

Abstract: Implied correlation and variance risk premium stand out in predicting market returns. However, while the predictive ability of implied correlation lasts for up to a year, the variance risk premium predicts market returns only for one quarter ahead. Contrary to the accepted view, implied correlation predicts the market return not through a diversification risk (average correlation) channel, but by predicting a concentration of market exposure, which defines the level of non-diversifiable market risk, or systematic diversification. Economy-wide implied correlation built exclusively from option prices of nine sector ETFs and the S&P500 efficiently predicts future market returns and systematic diversification risk in the form of market betas dispersion. Newly developed implied correlations for economic sectors provide industry-related information and are used to extract option-implied risk factors from sector-based covariances.

Abstract: Alternative assets, such as private equity, hedge funds, and real assets, are illiquid and opaque, thus posing a challenge to traditional models of asset allocation. In this paper, we study asset allocation and asset pricing in a general-equilibrium model with liquid assets and an alternative risky asset, which is opaque and incurs transaction costs, and investors who differ in their experience in assessing the alternative asset. We find that the optimal asset-allocation strategy of the relatively inexperienced investors is to initially tilt their portfolio away from the alternative asset and to hold more of it with experience. Counterintuitively, a decrease in the transaction cost for the alternative asset increases the portfolio tilt at the initial date, and hence, the liquidity discount. Transaction costs may induce inexperienced investors to hold a majority of the illiquid asset at later dates, even if they are pessimistic about future payoffs, and produce a sizable liquidity discount. During periods when the alternative asset is illiquid, investors trade the liquid equity index instead, leading to strong spillover effects.

Abstract: In this paper, we study the effect of proportional transaction costs on consumption-portfolio decisions and asset prices in a dynamic general equilibrium economy with a financial market that has a single-period bond and two risky stocks, one of which incurs the transaction cost. Our model has multiple investors with stochastic labor income, heterogeneous beliefs, and heterogeneous Epstein-Zin-Weil utility functions. The transaction cost gives rise to endogenous variations in liquidity. We show how equilibrium in this incomplete-markets economy can be characterized and solved for in a recursive fashion. We have three main findings. One, costs for trading a stock lead to a substantial reduction in the trading volume of that stock, but have only a small effect on the trading volume of the other stock and the bond. Two, even in the presence of stochastic labor income and heterogeneous beliefs, transaction costs have only a small effect on the consumption decisions of investors, and hence, on equity risk premia and the liquidity premium. Three, the effects of transaction costs on quantities such as the liquidity premium are overestimated in partial equilibrium relative to general equilibrium.

Abstract: We show how to extract the expected risk-neutral correlation between risk-neutral distributions of the market index (S&P 500) return and its expected volatility (VIX). Comparing the implied correlation with its realized counterpart reveals a significant index-to-volatility correlation risk premium. It compensates for the fear of rising and enduring volatility due to market crashes and measures a new dimension of risk not covered by other variables. The correlation risk premium asymmetrically focuses on tail risk, unlike the variance risk premium. Incorporating information from both equity and volatility markets, it predicts future index returns and changes in both future returns and volatilities.

Abstract: Motivated by extensive evidence that stock-return correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. We propose a direct and intuitive test by comparing option-implied correlations between stock returns (obtained by combining index option prices with prices of options on all index components) with realized correlations. Our parsimonious model shows that the substantial gap between average implied (38% for S&P500 and 44% for DJ30) and realized correlations (31% and 34%, respectively) is direct evidence of a large negative correlation risk premium. Empirical implementation of our model also indicates that the index variance risk premium can be attributed to the high price of correlation risk. Finally, we provide evidence that option-implied correlations have remarkable predictive power for future stock market returns.

Abstract: We study whether option-implied conditional expectation of market loss due to tail events, or tail loss measure, contains information about future returns, especially the negative ones. Our tail loss measure predicts future market returns, magnitude and probability of the market crashes, beyond and above other option-implied variables. Stock-specific tail loss measure predicts individual expected returns and magnitude of realized stock-specific crashes in the cross-section of stocks. Investor, especially the one caring about the left tail of her wealth distribution (e.g., disappointment-averse), benefits from using the tail loss measure as an information variable to construct managed portfolios of risk-free asset and market index. The tail loss measure is motivated by the results of the extreme value theory, and it is computed from observed prices of out-of-the-money put as the risk-neutral expected value of a loss beyond a given relative threshold.

Abstract: Our objective in this paper is to examine whether one can use option-implied information to improve the selection of mean-variance portfolios with a large number of stocks, and to document which aspects of option-implied information are most useful for improving their out-of-sample performance. Portfolio performance is measured in terms of four metrics: volatility, Sharpe ratio, certainty-equivalent return, and turnover. Our empirical evidence shows that using option-implied volatility helps to reduce portfolio volatility; option-implied correlation does not improve any of the metrics; and, expected returns estimated using information in option-implied volatility and option-implied skewness increase substantially both the Sharpe ratio and certainty-equivalent return, even after prohibiting shortsales and accounting for transactions costs.

Abstract: Using data on all U.S. exchange-traded individual stock options, we show that the currently observed option-implied ex ante skewness is positively related to future stock returns. This contrasts with the existing evidence that uses historical stock or option data to estimate skewness and ﬁnds a negative skewness-return relation. We compute the ex ante skewness using the model-free implied skewness (MFIS) as in Bakshi, Kapadia, and Madan (2003) and show that high MFIS stocks outperform low MFIS stocks by 45 basis points per month after correcting for systematic exposure. We ﬁnd that the positive MFIS-return relation stems from the ability of the current MFIS to identify the deviation of a ﬁrm’s value from its fundamental value, and the most overvalued stocks have the most negative ex ante skewness. We further ﬁnd that the speed of the value correction process depends on the arbitrage risk faced by arbitrageurs trying to exploit the observed inefficiencies. Our results have implications for the segmentation of equity and options markets as well as for limits of arbitrage in equity markets.